Molecular mechanisms of protein aggregation from global fitting of kinetic models


The elucidation of the molecular mechanisms by which soluble proteins convert into their amyloid forms is a fundamental prerequisite for understanding and controlling disorders that are linked to protein aggregation, such as Alzheimer's and Parkinson's diseases. However, because of the complexity associated with aggregation reaction networks, the analysis of kinetic data of protein aggregation to obtain the underlying mechanisms represents a complex task. Here we describe a framework, using quantitative kinetic assays and global fitting, to determine and to verify a molecular mechanism for aggregation reactions that is compatible with experimental kinetic data. We implement this approach in a web-based software, AmyloFit. Our procedure starts from the results of kinetic experiments that measure the concentration of aggregate mass as a function of time. We illustrate the approach with results from the aggregation of the β-amyloid (Aβ) peptides measured using thioflavin T, but the method is suitable for data from any similar kinetic experiment measuring the accumulation of aggregate mass as a function of time; the input data are in the form of a tab-separated text file. We also outline general experimental strategies and practical considerations for obtaining kinetic data of sufficient quality to draw detailed mechanistic conclusions, and the procedure starts with instructions for extensive data quality control. For the core part of the analysis, we provide an online platform ( that enables robust global analysis of kinetic data without the need for extensive programming or detailed mathematical knowledge. The software automates repetitive tasks and guides users through the key steps of kinetic analysis: determination of constraints to be placed on the aggregation mechanism based on the concentration dependence of the aggregation reaction, choosing from several fundamental models describing assembly into linear aggregates and fitting the chosen models using an advanced minimization algorithm to yield the reaction orders and rate constants. Finally, we outline how to use this approach to investigate which targets potential inhibitors of amyloid formation bind to and where in the reaction mechanism they act. The protocol, from processing data to determining mechanisms, can be completed in <1 d.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Key steps of the protocol.
Figure 2: Flowchart of the protocol.
Figure 3: The power of global fitting.
Figure 4: Data unsuitable for analysis.
Figure 5: Half-times as a guide to mechanisms.
Figure 6: Mechanisms and models.
Figure 7: Fitting flowchart.


  1. 1

    Knowles, T.P.J., Vendruscolo, M. & Dobson, C.M. The physical basis of protein misfolding disorders. Phys. Today 68, 36 (2015).

    CAS  Article  Google Scholar 

  2. 2

    Chiti, F. & Dobson, C.M. Protein misfolding, functional amyloid, and human disease. Annu. Rev. Biochem. 75, 333–366 (2006).

    CAS  Article  Google Scholar 

  3. 3

    Dobson, C.M. Protein folding and misfolding. Nature 426, 884–890 (2003).

    CAS  Article  Google Scholar 

  4. 4

    Aguzzi, A. & Haass, C. Games played by rogue proteins in prion disorders and Alzheimer's disease. Science 302, 814–818 (2003).

    CAS  Article  Google Scholar 

  5. 5

    Aguzzi, A. & O'Connor, T. Protein aggregation diseases: pathogenicity and therapeutic perspectives. Nat. Rev. Drug Discov. 9, 237–248 (2010).

    CAS  Article  Google Scholar 

  6. 6

    Hardy, J. & Selkoe, D.J. The amyloid hypothesis of Alzheimer's disease: progress and problems on the road to therapeutics. Science 297, 353–356 (2002).

    CAS  Article  Google Scholar 

  7. 7

    Hu, X. et al. Amyloid seeds formed by cellular uptake, concentration, and aggregation of the amyloid-beta peptide. Proc. Natl. Acad. Sci. USA 106, 20324–20329 (2009).

    CAS  Article  Google Scholar 

  8. 8

    Fersht, A.R. Structure and Mechanism in Protein Science. (W.H. Freeman,1999).

  9. 9

    Ferrone, F.A., Hofrichter, J. & Eaton, W.A. Kinetics of sickle hemoglobin polymerization. II. A double nucleation mechanism. J. Mol. Biol. 183, 611–631 (1985).

    CAS  Article  Google Scholar 

  10. 10

    Oosawa, F. & Asakura, S. Thermodynamics of the Polymerization of Protein (Academic Press, 1975).

  11. 11

    Knowles, T.P.J. et al. An analytical solution to the kinetics of breakable filament assembly. Science 326, 1533–1537 (2009).

    CAS  Article  Google Scholar 

  12. 12

    Cohen, S.I.A. et al. The molecular chaperone brichos breaks the catalytic cycle that generates toxic Aβ oligomers. Nat. Struct. Mol. Biol. 22, 207–213 (2015).

    CAS  Article  Google Scholar 

  13. 13

    Arosio, P., Vendruscolo, M., Dobson, C.M. & Knowles, T.P.J. Chemical kinetics for drug discovery to combat protein aggregation diseases. Trends Pharmacol. Sci. 35, 127–135 (2014).

    CAS  Article  Google Scholar 

  14. 14

    Arosio, P., Meisl, G., Andreasen, M. & Knowles, T.P.J. Preventing peptide and protein misbehavior. Proc. Natl. Acad. Sci. USA 112, 5267–5268 (2015).

    CAS  Article  Google Scholar 

  15. 15

    Ruschak, A.M. & Miranker, A.D. Fiber-dependent amyloid formation as catalysis of an existing reaction pathway. Proc. Natl. Acad. Sci. USA 104, 12341–12346 (2007).

    CAS  Article  Google Scholar 

  16. 16

    Cohen, S.I.A. et al. Nucleated polymerization with secondary pathways. I. Time evolution of the principal moments. J. Chem. Phys. 135, 065105 (2011).

    Article  Google Scholar 

  17. 17

    Cohen, S.I.A., Vendruscolo, M., Dobson, C.M. & Knowles, T.P.J. Nucleated polymerization with secondary pathways. II. Determination of self-consistent solutions to growth processes described by non-linear master equations. J. Chem. Phys. 135, 065106 (2011).

    Article  Google Scholar 

  18. 18

    Meisl, G. et al. Differences in nucleation behavior underlie the contrasting aggregation kinetics of the aβ40 and aβ42 peptides. Proc. Natl. Acad. Sci. USA 111, 9384–9389 (2014).

    CAS  Article  Google Scholar 

  19. 19

    Abelein, A., Graslund, A. & Danielsson, J. Zinc as chaperone-mimicking agent for retardation of amyloid β peptide fibril formation. Proc. Natl. Acad. Sci. USA 112, 5407–5412 (2015).

    CAS  Article  Google Scholar 

  20. 20

    Cohen, S.I.A., Vendruscolo, M., Dobson, C.M. & Knowles, T.P.J. From macroscopic measurements to microscopic mechanisms of protein aggregation. J. Mol. Biol. 421, 160–171 (2012).

    CAS  Article  Google Scholar 

  21. 21

    Fowler, D.M., Koulov, A.V., Balch, W.E. & Kelly, J.W. Functional amyloid—from bacteria to humans. Trends Biochem. Sci. 32, 217–224 (2007).

    CAS  Article  Google Scholar 

  22. 22

    Cremades, N. Direct observation of the interconversion of normal and toxic forms of α-synuclein. Cell 149, 1048–1059 (2012).

    CAS  Article  Google Scholar 

  23. 23

    Michaels, T.C.T. & Knowles, T.P.J. Role of filament annealing in the kinetics and thermodynamics of nucleated polymerization. J. Chem. Phys. 140, 214904 (2014).

    Article  Google Scholar 

  24. 24

    Scheibel, T., Bloom, J. & Lindquist, S.L. The elongation of yeast prion fibers involves separable steps of association and conversion. Proc. Natl. Acad. Sci. USA 101, 2287–2292 (2004).

    CAS  Article  Google Scholar 

  25. 25

    Esler, W.P. et al. Alzheimer's disease amyloid propagation by a template-dependent dock-lock mechanism. Biochemistry 39, 6288–6295 (2000).

    CAS  Article  Google Scholar 

  26. 26

    Oosawa, F. & Kasai, M. A theory of linear and helical aggregations of macromolecules. J. Mol. Biol. 4, 10–21 (1962).

    CAS  Article  Google Scholar 

  27. 27

    Wales, D.J. & Doye, J.P.K. Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms. J. Phys. Chem. A 101, 5111–5116 (1997).

    CAS  Article  Google Scholar 

  28. 28

    Cohen, S.I.A. et al. Proliferation of amyloid-β42 aggregates occurs through a secondary nucleation mechanism. Proc. Natl. Acad. Sci. USA 110, 9758–9763 (2013).

    CAS  Article  Google Scholar 

  29. 29

    Paolo Arosio, P., Cukalevski, R., Frohm, B., Knowles, T.P.J. & Linse, S. Quantification of the concentration of aβ42 propagons during the lag phase by an amyloid chain reaction assay. J. Am. Chem. Soc. 136, 219–225 (2014).

    Article  Google Scholar 

  30. 30

    Walsh, D.M. et al. A facile method for expression and purification of the Alzheimer's disease-associated amyloid β-peptide. FEBS J. 276, 1266–1281 (2009).

    CAS  Article  Google Scholar 

  31. 31

    Finder, V.H., Vodopivec, I., Nitsch, R.M. & Glockshuber, R. The recombinant amyloid-beta peptide Aβ1-42 aggregates faster and is more neurotoxic than synthetic Aβ1-42. J. Mol. Biol. 396, 9–18 (2010).

    CAS  Article  Google Scholar 

  32. 32

    Cukalevski, R. et al. Role of aromatic side chains in amyloid β-protein aggregation. ACS Chem. Neurosci. 3, 1008–1016 (2012).

    CAS  Article  Google Scholar 

  33. 33

    Hellstrand, E., Boland, B., Walsh, D.M. & Linse, S. Amyloid β-protein aggregation produces highly reproducible kinetic data and occurs by a two-phase process. ACS Chem. Neurosci. 1, 13–18 (2010).

    CAS  Article  Google Scholar 

Download references


This work was supported by grants from the Swedish Research Council (VR) and its Linneaus Centre Organizing Molecular Matter (S.L.), the European Research Council (S.L. and T.P.J.K.), the Cambridge Home and EU Scholarship Scheme (G.M.), the Frances and Augustus Newman Foundation (T.P.J.K.) and the Biotechnology and Biological Sciences Research Council (T.P.J.K.), St. John's College Cambridge (T.C.T.M. and T.P.J.K.) the Marie Curie Intra-European Fellowship scheme (P.A.), and the Engineering and Physical Sciences Research Council (J.B.K.). We thank the members of the Knowles and Linse research groups for their input and testing of the program, in particular X. Yang, R. Gaspar, T. Mueller, P. Flagmeier and G.R. McInroy.

Author information




G.M., T.P.J.K. and M.V. conceived the project; G.M. and J.B.K. wrote the software; G.M., J.B.K., S.L., C.M.D. and T.P.J.K. wrote the paper; G.M., P.A. and T.C.T.M. designed the analysis in the presence of binders.

Corresponding author

Correspondence to Tuomas P J Knowles.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Methods

Advice regarding data layout, interpreting half times and scalings, and integrated rate laws and approximate scalings (PDF 1292 kb)

Supplementary Data

An example of data appropriately formatted for use with Amylofit (TXT 53 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Meisl, G., Kirkegaard, J., Arosio, P. et al. Molecular mechanisms of protein aggregation from global fitting of kinetic models. Nat Protoc 11, 252–272 (2016).

Download citation

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing